Then it hangs and I have to reinsert the battery. I have no clue what this means... I've googled without any luck (well, I read about som guys with the same error but they just "solved" it with getting a new NXJ brick) and I've also tried with anorther version of the firmware (both 0.4beta and 0.3alpha).

My NXT started giving me the exact same error message yesterday. The strange thing is that it would run any programs that had been uploaded before the point where it crashed, but after that all uploaded programs would result in the error message being displayed.

Luckily I managed to fix the problem by reinstalling the Lejos firmware. Maybe you should try doing that again?